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Generating Curves of Minimal Ruled Real Hypersurfaces in a Nonflat Complex Space Form

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  09 January 2019

Sadahiro Maeda ,
Hiromasa Tanabe  and
Seiichi Udagawa
Sadahiro Maeda
Affiliation:
Department of Mathematics, Saga University, 1 Honzyo, Saga 840-8502, Japan Email: sayaki@cc.saga-u.ac.jp
Hiromasa Tanabe
Affiliation:
Department of Science, National Institute of Technology, Matsue College, Matsue, Shimane 690-8518, Japan Email: h-tanabe@matsue-ct.jp
Seiichi Udagawa
Affiliation:
Department of Mathematics, School of Medicine, Nihon University, Itabashi, Tokyo 173-0032, Japan Email: udagawa.seiichi@nihon-u.ac.jp
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Abstract

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We first provide a necessary and sufficient condition for a ruled real hypersurface in a nonflat complex space form to have constant mean curvature in terms of integral curves of the characteristic vector field on it. This yields a characterization of minimal ruled real hypersurfaces by circles. We next characterize the homogeneous minimal ruled real hypersurface in a complex hyperbolic space by using the notion of strong congruency of curves.

Keywords

nonflat complex space formminimal ruled real hypersurfaceconstant mean curvatureintegral curves of the characteristic vector field

MSC classification

Primary: 53B25: Local submanifolds
Secondary: 53C40: Global submanifolds
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 2 , June 2019 , pp. 383 - 392
Copyright
© Canadian Mathematical Society 2018 

References

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